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  3. Foundations of Probability in R
  • 1

    The binomial distribution

    Kostenlos

    One of the simplest and most common examples of a random phenomenon is a coin flip: an event that is either "yes" or "no" with some probability. Here you'll learn about the binomial distribution, which describes the behavior of a combination of yes/no trials and how to predict and simulate its behavior.

  • 2

    Laws of probability

    In this chapter you'll learn to combine multiple probabilities, such as the probability two events both happen or that at least one happens, and confirm each with random simulations. You'll also learn some of the properties of adding and multiplying random variables.

  • 3

    Bayesian statistics

    Bayesian statistics is a mathematically rigorous method for updating your beliefs based on evidence. In this chapter, you'll learn to apply Bayes' theorem to draw conclusions about whether a coin is fair or biased, and back it up with simulations.

  • 4

    Related distributions

    So far we've been talking about the binomial distribution, but this is one of many probability distributions a random variable can take. In this chapter we'll introduce three more that are related to the binomial: the normal, the Poisson, and the geometric.

Initializing

Übung

Simulating from the binomial and the normal

In this exercise you'll see for yourself whether the normal is a reasonable approximation to the binomial by simulating large samples from the binomial distribution and its normal approximation and comparing their histograms.

Anweisungen

100 XP
  • Generate 100,000 draws from the Binomial(1000, .2) distribution. Save this as binom_sample.
  • Generate 100,000 draws from the normal distribution that approximates this binomial distribution, using the rnorm() function. (Remember that rnorm() takes the mean and the standard deviation, which is the square root of the variance). Save this as normal_sample.
  • Compare the two distributions with the compare_histograms() function. (Remember that this takes two arguments: the first and second vectors to compare).